hello everyone thank you for the

opportunity to make this presentation today I will talk about sequential

multiple assignment randomized trial with a short name SMART trial this is a

novel clinical trial design for compare multiple adaptive intervention and we

introduced the concept give several examples and talk about methods to

design and analyzing this trial so the concept of personalized medicine is an

increasing popular topic into this healthcare research individualizing

patient care is particularly important in managing chronic diseases the patient

care in chronic disease typically take a long period of time during which

multiple clinical factors vary across different patient at a different time

within the same patient these clinical factors can be medication adherence, side

effects, intermediate response, and a history of previous treatment patient

received in early of the period the key to success in managing chronic disease

is to design a flexible treatment strategy that can adapt to patients

personal information for example we need a strategy to help adjust the inherent

heterogeneity across different patient and help control the variability within

the patient across time ideally the strategy should be able to help us

improve the individual compliance to the treatment patient receive and minimize

the burden and cost so this kind of study strategy fits the paradigm of

personalized medicine the chronical disease, the clinical practice of chronical

disease, such as cancer care and depression management clinician

often need to make a sequence of treatment decision

throughout the entire course of patient clinical care

this decision usually adapt to a patient’s treatment and a covariant

history in previous stage in the same treatment so adaptive intervention formalizes

mechanic of such a sequence of decision-making here is an example of

two-stage adaptive intervention designed for a newly diagnosed patient with the

Diffuse Large B-Cell Lymphoma this is originally reported by Habermann in 2006

and published in JCO. under this adaptive intervention, patient was first given

CHOP: a combination of four chemotherapy agent for eight cycles at

stage one, at the end of stage one, the patients will classify as responders and

non-responders here response is defined as complete remission or partial

remission and non-response otherwise for now responders they will be given

Rituximab, they were given G-CSF for supportive at the stage two and for

responders they will give Rituximab for six months as a maintanence this is one

adaptive intervention and an intervention can be recommended to all

the patient with newly diagnosed Diffuse Large B-Cell Lymphoma

a patient under this adaptive intervention in clinical practice can

possibly receive two treatment sequence one is CHOP-Response

Rituximab and the other is CHOP-No Response

G-CSF specifically which treatment sequence a patient will follow in

practice depending on value of intermediate response observed on this

patient. The adaptive intervention typically has four important components.

first it has multiple treatment stage each treatment stage refers to an

interval of time during which a patient receive one specific treatment for

example in this case we can see at a stage one, all the patient will receive

one treatment which is CHOP while at the stage two a part of the patients

will receive Rituximab and rest of them receive G-CSF

in the practice researchers can define a number of stage

of adaptive intervention depending on a feature of patient care and interests of

study also an adaptive intervention has a sequence of decisions regarding to the

treatment selection for example in this case at the stage two a decision needs

to be made is if a patient failed to respond at the end of stage one which

treatment should be selected for next stage well if the patient achieved

stabilized which main treatment should be selected for maintenance the stage one

treatment here is not adaptive to any baseline information for surely we can

design another adaptive decision at stage 1 for example we can give patient

with comorbidity a certain treatment and for those patients without comorbidity

another type of treatment in that case we’ll receive four treatment sequence in

this adaptive intervention which was more complicated also adaptive intervention

has a set of treatment option at a decision-making point so can choose

different treatment based on patients different clinical information this

option can be dose-type or timing of medication given to patient if there’s

only one treatment option then different patient based on different

clinical condition is not meaningful in adaptive intervention also we have

tailoring variable which is variable that contains

information to support the decision making in adaptive intervention for

example in this case the tailoring variable to the supported decision-making at the

stage two is the response to CHOP measure at the end of stage 1 so we

based on the patient’s response to decide which treatment we give to this

patient at the second stage a commonly seen kind of variable in adaptive

intervention include baseline covariates, previous treatments

side effect, and a medication adherence so we for the example I give in previous

slides and the four important components is easy to understand the official

concept of adaptive intervention here adaptive intervention it’s a multi stage

treatment strategy consisting of a sequence of decision-making rules one

per stage of intervention which is specifying how to adapt the treatment

selection according to individual patients clinical history of treatment

other covariates so statistics play important role in the

adaptive intervention research it provides the evidence base or we can call

this data-driven framework to help us optimize the decision-making for

treatment selection for individual in adaptive intervention also it help us

identify the optimal adaptive intervention leading to the best how

come in a long run. a natural question in adaptive intervention research is

whether or not an adaptive intervention identified in the study is

better than the others so in terms of statistics we can transfer the question

into whether a particular adaptive intervention can lead to a better

average outcome in the long run. to answer this question we can we need to

conduct a causal inference based on a sample data collect from study it can be

true type of study one is observational study and the other is randomized

clinical trial in observational study, the data is relatively easy to obtain

and with low cost however the reason that a patient received a specific

treatment in observational study it’s not always completely documented so the

conclusion made based on observational data sometimes can be biased potentially

unfortunately the existence of the impact from a measure confounded the

observational study is not numerically testable because we don’t even have the

data so we cannot conduct the test so the finding in observational study need

to be verified using the result of randomized clinical trial. in a

randomized clinical trial the reason that a patient was assigned a treatment is

because, is a result of randomization so the randomization

procedure can help us rule out the impact from a major confounder

so we can use the data directly to support the causal inference. today’s

presentation we talked about the design for randomized clinical trial. sequential

multiple assignment randomized trial with a short name SMART

trial is a clinical trial design that can be used to compare multiple adaptive

intervention such a design randomly assign patients to a collection of adaptive

intervention that may overlap in terms of treatment decision so by the virtue of

randomization this design provided information allow us to compare multiple

adaptive intervention directly in a study you can see here is an example of

two-stage SMART for those being former patient. under this design pressure

who enroll in the trial will first randomized to receive CHOP or R-CHOP

which is Rituximab-CHOP for eight cycles at stage one. at the end of stage

one the intermediate evaluation was given to each patient and the patient

will classify as responders and non-responders

based on the definition we mentioned in previous slides. for non-responders in

this study at the stage two they all given G-CSF

for supportive while for those responders they will be randomized again to receive

Rituximab or observation for maintenance at stage 2 we can see there are six

treatment sequence embedded in this design diagram presented as the arrow goes

from left to the right and we denote it by sequence A, B, C to F. for example sequence

A is CHOP response Rituximab so a patient

who complete this trial will follow one of this six treatment sequence depending

on the result of randomization and intermediate response. the previous

example of two stage at active intervention is highlighted in red in

this design diagram by which we give patient CHOP at the stage one, Rituximab

at the stage two if the patient respond and a G-CSF at the stage two

if the patient fail to respond so we denote this adaptive intervention

as (A+C) here because it consists to treatment sequence, sequence

A and sequence C. similarly we can identify another three adaptive

intervention in this design diagram each adaptive intervention consists twp

treatment sequences one for response and one for no response and both treatment

sequence share the same stage one treatment. for example we

can identify another adaptive intervention by giving people CHOP at stage one,

observation at stage 2 if the patient respond and G-CSF

at stage 2 if a patient fail to respond if you look at the design diagram

we can see both these two adaptive strategy, they actually share the same

treatment sequence which was sequence C here so that is to say for those

patient who receive CHOP at the stage one fail to respond and receive G-CSF at

the stage two actually contributed information that helped us to evaluate

two adaptive intervention. this feature makes SMART a very efficient design but

also introduced some complicity in statistical inference and we talked more

detail about it the curse of dimensionality is the major concern of

SMART design because the total number of adaptive intervention identified in

SMART increase exponentially as the number of

treatment option and intermediate response categories increases for example in this

study we can identify for adaptive

interventions however we will modify this a little bit we increase one

treatment option for those patient who fail to respond to stage one treatment

so the total number of intervention will increase immediately from four to eight

which is substantial. this feature has big impact in a statistical inference in

terms of control of false positive finding and I will talk more about it so

in a clinical trial practice there are some other clinical designs more or less

to share some common feature with SMART the similarity between SMART designs and

these designs sometimes cost confusion for clinical trialists

who gets to know this concept at the beginning these are also the playground

that we statisticians receive a lot of questions from our clinician and

collaborators. today I will compare SMART design with two clinical trial designs:

crossover and adaptive design so by making these comparisons we further

demonstrate the feature of SMRT designs here. so first we look at a crossover

design which is a repeated measure randomized clinical trial design that

each individual in this study will receive variant treatment sequence

across multiple stage here is an example of crossover study compared two fixed

treatment A and B at the beginning of stage one patients were randomized to

receive A or B at the stage one. at the end of stage one the primary outcome was

measure for each patient and then patients with switch from A to B from B

to A at the stage two and repeat a same story at the second stage so

operationally crossover design is somewhat similar to SMART because in

this design patients also receive different treatments across multiple

stage however we can clearly separate these two designs from three aspects so

first of all crossover design is motivated by improved efficiency and

reduce the total sample of the study but the goal is still try to compare two fixed

treatments We can call this two non-adaptive

intervention for example in this case although different patients receive

treatment sequence of A to B or B to A this design is just try to take two measures

from each patient and the goal is to reduce the total sample size by still with

their primary hypothesis to compare treatment A and B however the SMART is

designed to compare multiple adaptive intervention which is different from

crossover also in a crossover design the treatment assignment only depends on the

baseline style randomization in this case patients either received treatments A to B

or sequence B to A but which sequence the patient will follow completely

depends on the baseline randomization once the trial is star will never change

it unless the patient drop out however in a SMART the story is totally different

only the set of decision rules about how to

assing treatment is pre-specified at the baseline because the randomization

is conducted sequentially at the beginning of every stage so until the

last decision is made is unlikely to know each patient follow what kind of

treatment sequence so also the major pitfall of crossover design is something

called carryover effects which is the prior effect of treatment A or B can be

confounded with the succeeding treatment effect of B or A so in this case if the

carryover effect exists so when we look at the primary outcome at

the end of stage two we won’t be able to know if the primary outcome is

purely because the treatment patient received at the stage two or is partly

because treatment a patient received at the

first stage which is reduced the power of the study so to avoid the

contamination of carryover effect in a crossover design the typically insert a

unique component called wash over a period between two two treatment stage

the key to set up a wash over period is to control the time

window large enough to eliminate any possible carryover effects on the other

hand in order to make the trial efficient once this requires is made we

also need to try to control the time window as short as possible. in a SMART

is different because the SMART design is trying to compare the effects of adaptive

intervention and the effect of adaptive invention is possibly due to the

interaction effect between the treatment a patient received in different stage so

in SMART we do not set up any washout period to try to rule out the carryover

effects another term that sometimes get confused with SMART is adaptive design

in fact adaptive design is an umbrella term that covers a family of randomized

clinical trial. the members in the family including continuously assessment design,

sample size recalculation design, or adaptive randomization design all this

design has one common feature which is they try to modify some of the design

aspects such as total sample size randomization scheme based on the result

of interim analysis the goal of this adaptive design is trying to improve the

overall quality of patient care in favor of those treatment to show better

evidence of better efficacy or less toxicity from the interim analysis so

the between subject information is adaptive while in a SMART what we adapt

is with-in subject information between different stage but a common design

element like total sample size randomization scheme are all fixed we do not

change it once the study is start so after introduced the concept of

adaptive intervention and SMART trial next I will talk about methods to

design SMART and analyzing SMART data first I will talk about how to estimate

the adaptive intervention value with two methods such as maximum likelihood estimator

and inverse probability weighting estimator

then I will talk about how to conduct the hypothesis test in SMART to compare

multiple adaptive intervention I will talk about pairwise test also global test or

call omnibus test then I will talk about how to conduct the sample size

calculation in designing a SMART trial so before the illustrative method, first let’s

take a look at the general scheme of two stage SMART this is the scheme that we

used to conduct the statistical inference. Patient

enrolled in the trial was first randomized to any treatment option at stage one, we denoted

by T1, T2 to Ti for each stage one treatment the certain number of

intermediate response categories follow it in a general SMART design we allow the number

of intermediate response categories to vary by different stage

one treatment for example under T1 where J1 intermediate response

categories Denoted by R11, R12 to R1j1

while under Ti we have ji intermediate response categories denoted by our Ri1, Ri2 to

Riji similarly where are the number of stage 2 treatment option can be varied

by different history of stage 1 treatment and intermediate response

suppose a patient enroll in the trial received T1 at the stage 1 and had intermediate

response R11 at the stage two based on this design patient will be

randomized to receive one out of K11 treatment option denoted by S111,

S112 to S11K11 here. so in the lymphoma trial I just talked

about we have two treatment option at stage 1 so T1 will be CHOP and T2

will be R-CHOP because we defined the intermediate response for both stage 1

treatment as a binary outcome so after T1 we’ll have 2 bullets here with R11 which

represent the response and R12 will represent no response

similarly after T2, we have two bullets with R21 corresponding to

response and R22 responding to no response for the stage-two treatment

because we do not randomized non-responders again

so following R12 and R22 we’ll have one bullet of treatment option

while for those responders who will be randomized to two treatment option so we

have two bullets here following along one and another two bullets for R21

so data collected from the general scheme of two-stage SMART for a patient

can be summarized as a longitudinal trajectory across time (U,X,V,Y) where U is

the variable represent the stage one treatment, X is the intermediate

response, V is the stage two treatment and Y is the final primary outcome so to

do the statistical inference we assume (U,X,V,Y) are independent and

identically distributed with pi_i being the stage one randomization

probability corresponding to the patient received TI at the stage one. p_ij is the

intermediate response rate corresponding to R_ij given a patient received Ti at

the stage one and pi_ijk being the stage two randomization probability

corresponding to a patient receive S_ijk at a stage 2 given a patient received

TI the stage 1 had an intermediate response R_ij. finally we’ll see why the

primary outcome of interest follow given a history of Ti, R_ij, S_ijk follow a

distribution with mu_ijk in the parameter of interest and a tau_ijk being a

nuisance parameter so specifically in this presentation we just concern we just

focus on the mean of primary outcome as a parameter of interest

Suppose the primary outcome is a continuous variable Y given history of Ti, R_ij, S_ijk

will follow a normal distribution with mu_ijk being the mean of

primary outcome which is the parameter of interest and variance sigma_ijk squared.

so under this framework each adaptive intervention consists a series of

treatment sequences with each of the sequence there’s a specific mean of

primary outcome corresponding to it and we denote it by mu all these sequence

share the same stage one treatment we define the value of adaptive intervention

as a weighted sum of this treatment sequence specific mean mu weighted by

the intermediate response rate P so value of adaptive intervention can be

interpreted as the average primary outcome across all the possible

treatment a patient can receive under the adaptive intervention now let’s take

a look at the lymphoma trial example suppose we are interested in

calculate the value for adaptive intervention A plus C we have two treatment

sequence here sequence A and C so have two sequence specific mean denoted by mu_A

and mu_C let P1 be the intermediate response rate following CHOP so the value of

adaptive intervention A plus C can be calculated by P1 which is the

probability that we will observe a patient who following sequence A under

this adaptive intervention multiply the mean of sequence mu_A plus 1 minus P1

which is the probability that we observe a patient following sequence C under

this adaptive intervention multiplied by mu_C similarly we can calculate the

value of other three adaptive intervention as we show in the bottom of

these slides. to estimate a value of adaptive intervention we can use maximum

likelihood estimator MLE the MLE of theta adaptive intervention

value can be obtained by plugging the MLE of those intermediate response rate

P and MLE of of sequence-specific mean mu. the MLS of P and mu can be

obtained by maximizing the joint distribution of (U,X,V,Y). alternatively we

can use another method to estimate the value of adaptive intervention this is

inverse probability weighted estimator using formula one in the top of the

slide. here W is the inverse probability treatment ways assigned to each patient

following complete SMART trial where l is the observed primary outcome

observed in patient l. l is the indicator of each subject who complete a SMART

trial with value 1 to n and it’s the total number of patient who completed the

trial to build the inverse probability treatment weights for those patient who

follow a sequence not belonging to the adaptive intervention of interest we

similarly give this patient a weight of 0 while for those patient who follow a

sequence belonging to the adaptive intervention we’re interesting in the

weight can be built based on a cumulative product of inverse randomization

probability corresponding to all the treatment a patient received in the

study formula 3 is the formula to calculate

the variance estimator of a IPWE we can see this is a function of M total sample

size, W inverse probability treatment weight and Y observe primary outcome so let’s

go through the lymphoma trial and see how we construct the weights to calculate

the inverse probability weighted estimator

suppose we’re interesting in the adaptive innovation A+C we have three

randomization probability here pi_1 corresponding to CHOP at the stage 1

pi_2 corresponding to Rituximab for those responders of CHOP and pi_3

corresponding to the Rituximab corresponding to those R-CHOP

pi_1 and pi_2 will be related to calculate the weights for those patient who

following adaptive intervention A+C For patient who follow sequence A here

they had two randomization in the study one in stage 1 and one in stage two so

the weight can be calculated using one over pi_1 multiply 1 over pi_2 to

make it simple, let’s assume pi_1, pi_2 and pi_3 are all equal to 50% so the weights for

those patient who follow treatment sequence A equal to 4 for those

patients who follow treatment sequence C the only randomization happens at the

beginning of stage 1 so for this patient the weight can be calculated by 1 over

Pi_1 which is 2 while for those patient who follow other treatment sequence not

belonging to this adaptive intervention B, D, E and F we simply give them weight

of 0 and then we plug in the formula can calculate the IPWE. so these two methods

to estimate the adaptive intervention value makes more likely estimator and

inverse probability weighting estimator they both consistent estimator and

asymptotically identical so when a sample size of a SMART is large enough

they have the same performance or at least similar performance compared to

the maximum likelihood estimator the calculation of IPW is relatively simple

because we can see the function only involve two components the randomization

probability and the observe primary outcome at the end of the study so we do not

have to deal with the complex structure of SMART also this method is robust to

the assumption of data distribution on the other hand the maximum likelihood

estimator take the advantage of asymptotic

efficiency when the assumption about data distribution correctly referred the

feature of sample data on the other hand if the assumption

about the distribution do not correctly reflect the feature of sample data that

the performance will go to the opposite way so I’ve done a lot of study in this

field and gained a lot of experience from the simulation study for SMART design

with moderate sample size where the primary outcome is continuous variable

or binary variable we can feel comfortable about the maximum likelihood

estimator and use this one so we take the advantage of asymptotic

efficiency so next I will talk a little about the distribution about MLEs which

is the fundamental theory of the statistical inference for comparison

here the upper case theta is the vector of all adaptive intervention value

embedded in a SMART design the lower case theta is a single adaptive intervention

value the subscript of theta is the indicator of each adaptive intervention

and G is the total number of adaptive intervention can be identified in a

SMART design so it can be pooled that the MLE of theta follow a multivariate

normal distribution asymptotically with variance covariance matrix sigma.

Sigma here is a block diagonal matrix of a series of small covariance matrix

denoted by Sigma_1, Sigma_2, to Sigma_i each of these small covariance matrix

corresponding to the MLEs of those adaptive intervention value share the same

stage 1 treatment in the study for example Sigma_1 here is the covariance

matrix of MLEs of all the adaptive intervention

starting with T1 at stage 1 these MLEs are correlated to each other due to the

overlap in structure and the correlation varies by study design. to compare

multiple adaptive intervention we can use a pairwise comparison by which we

conduct a series of pairwise tests to compare each pair of the adaptive

interventions the null hypothesis of pairwise test is

two adaptive interventions have the same value we can use formula four to

calculate the test statistics of a pairwise test here for denominator we

can plug in the estimator of adaptive intervention of two adaptive

interventions it can be a MLE or can be inverse probability weighted estimator

so for illustration purpose to make it simple for now I just focus on maximum

likelihood estimator. to calculate the variance, the denominator, if we

trying to compare two adaptive intervention do not overlap with each other in

structure the calculation is relatively easy because it only involve the

variance components when we try to compare two adaptive intervention there

are some more overlap in the design structure then the

computation will be a little more complicated because you need to involve

the cross product which is the covariance all this variance and

covariance information can be obtained from the estimate Sigma here so next I

will use a real data example to illustrate how we conduct the pairwise

comparison the data was collected the data was actually from a study called

CODIACS:comparison of depression intervention after accurate coronary

syndrome. this is a study that aimed to assess the quality of depression care of

different management program so the primary outcome of the study is

Beck Depression Inventory which is a continuous score, a higher

level of that Beck Depression Inventory indicating a more severity of depression

so an adaptive intervention relates to a more BDI reduction from baseline

indicating a better treatment effects so this is the design diagram of the study at

the stage one patient were randomized to receive medication and a behavioral

therapy for two months at the end of stage one patient were classified as

responders and non-responders based on the

reduction of BDI from baseline greater than three or no and then they will be

randomized again to receive medication and behavior therapy for another four

months based on different history of stage one treatment and intermediate

response this design structure provide data that allow us to evaluate up to

eight adaptive intervention. first we calculate the estimated adaptive

intervention to estimate the intervention value first we need to

estimate the response rate first we will estimate an intermediate

response rate following medication and behavioral therapy then we need to

calculate the sequence mean following each of those sequence then we plug in

the formula and calculate the MLE of all eight adaptive intervention as we

show here we can see the fifth adaptive intervention has the largest MLE so

we call this observed the best adaptive intervention. for the variance-covariance

matrix because we have eight adaptive intervention here this is actually a

block diagonal matrix with dimension eight by eight the small covariance matrix in

the upper left is the covariance matrix of those MLEs corresponding to the

intervention following medication at the stage one and then we have another four

adaptive intervention following behavioral therapy and variance

covariance matrix on the bottom right so a potential issue of using

pairwise comparison to evaluate all the adaptive innovation in SMART is this

procedure need to take into account multiple comparison issue

you see methods such as Bonferroni correction which is known to be

conservative when a number of adaptive intervention can be identified in SMART

increase for example in this case we can see suppose we try to compare the

adaptive intervention control overall significant level at 0.05 because

we have eight adaptive intervention so a pairwise comparison with Bonferroni

correction require a p-value less than 0.0018 to gain overall

significant. The last column of this table

give us all the p-values of pairwise tests to compare each adaptive

intervention with observed best which adaptive intervention five so you can

see but a comparison although there’s one p-value less than 0.05

after Bonferroni correction we cannot claim overall significant because there are

too many adaptive interventions this problem is particularly significant in

SMART because the sequential randomization of SMART always generate a

high dimensional data that are including a lot of adaptive interventions so

alternatively we can use a gatekeeping approach to do the analysis. A gatekeeping

approach is two-step approach in step one we conduct a global test or

sometime we call this omnibus test with the null hypothesis the older adaptive

intervention have the same value only if the

null hypothesis of the omnibus test was rejected we move

forward to do a selection otherwise we stop analysis a claim there’s no more

significant so here is the formula five is how we calculate the test statistics

Q for this global test and it’s the total sample size of patient who

complete SMART trial. C is the contrast matrix and I will talk about this later how

to construct it. Theta hat is the estimated value of all the adaptive intervention

and the Sigma hat is to estimate the asymptotic covariance matrix under the

null hypothesis, Q the test statistics will follow a chi square

distribution with the degrees of with a nu while under the alternative

hypothesis Q follow a non-central chi square distribution with

the non-centrality parameter lambda star the degrees of freedom of chi squared

test can be calculated using

formula 6 here summation of K_ij is the total number of stage 2 treatment

option and the summation J_i is the total number of intermediary response

categories. i is the total number of stage one treatment option let’s use the

example of CODIAC to see how we conduct a global test we have eight adaptive

intervention in this study so the null hypothesis of the global test is all

eight adaptive intervention have the same value to calculate the test

statistics first we need to construct the contrast matrix because we have

eight adaptive intervention the dimension of this contrast will be seven

by eight with each column of the matrix corresponding to one specific adaptive

intervention each row of this contrast each row of this contrast matrix

corresponding to one contrast to compare a pair of adaptive intervention in the

first row we compare adaptive intervention one versus intervention two in the

second row we compare intervention one with intervention three etc. once we have the contrast matrix we plug

in the formula with total sample size and estimated adaptive intervention

Theta hat and estimating asymptotic covariance matrix we can

calculate the test statistic Q equal to 36 to calculate the degrees of freedom

let’s go back to the design structure here we have eight treatment option at the

stage two, four intermediate response categories two stage one treatment

option so the degrees of freedom equal to 8 minus 4 plus 2 minus 1 which is

equal to 5 by this means we finally obtain a

p-value of global test less than 0.001 because it’s

more powerful than pairwise tests and we can claim overall significant in this

study. another good thing about the global test is a provide efficient

method that can help us power a SMART trial here is the general approach to

conduct the sample size calculation for SMART trial to conduct the sample size

calculation first we need to specify with the designd structure statistician

communicate with clinical collaborators and if our finalized the design

structure what will be the treatment option at the stage one in a stage two

how to define the intermediate response and then we need to set up the

randomization probability ties once we finalize the design structure we need to

obtain lambda star which is the non centrality parameter and

other alternative hypotheses in step two to obtain the value of lambda star we

need to solve the equation of seven to do this with the pre-specified the

target type one error rate alpha and target power minus beta and then we need

to calculate the effect signs Delta using formula eight here C is the contrast

matrix we just saw. Theta star is the target adaptive

intervention value and a sigma star is the target asymptotic variance covariance

matrix once you have the value of lambda star and the Delta we divide the lambda

star by Delta we can obtain n which is the total sample size of all the

patients who we require for SMART trial another good thing about

SMART trial is other than it is a very efficient a design for comparing

multiple adaptive intervention the study design also provide a very rich

information that allow to answer a series

of secondary research question for example in this study the Lymphoma

Trial, the primary interest question is compare four adaptive intervention but

we can also use the data to compare CHOP and R-CHOP to see which one provides a

better response rate for the patient with newly diagnosed lymphoma also we

can compare Rituximab vs. observation for those responders of CHOP and compare

Rituximab and observation for those responders after R-CHOP we

can do this is because we conduct sequential randomization given different

conditions of the patients sequentially in the study

although the trial was powered based on the primary question so when we study

this secondary question we may not have enough power to control the study under

a very restrict of the type of one error

however we also still provided a very rich valuable information for those

questions this is another example that we use SMART design to improve the

design efficiency compared to a traditional randomized clinical trial

because the time of limit I will skip this one if anyone who is interested in

it you can contact me after the presentation and I will very pleased to

talk about it so in summary SMART is efficient randomized clinical trial

design that provide data to compare multiple adaptive interventions also

other than answering primary question it also provides rich information to answer

a series of secondary question in terms of patient care of chronic disease in

statistics in the last 10 years many study has been conducted in this field

and several important paper has been published so the technique for design in

a SMART trial and analyzing SMART data is getting mature so it will be a good

time to conduct this clinical trial design in the clinical practice of

medical research so it has a broad application potentially in the future

these are the reference of today’s presentation. thank you